Annals of Statistics

Empirical Likelihood is Bartlett-Correctable

Thomas DiCiccio, Peter Hall, and Joseph Romano

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It is shown that, in a very general setting, the empirical likelihood method for constructing confidence intervals is Bartlett-correctable. This means that a simple adjustment for the expected value of log-likelihood ratio reduces coverage error to an extremely low $O(n^{-2})$, where $n$ denotes sample size. That fact makes empirical likelihood competitive with methods such as the bootstrap which are not Bartlett-correctable and which usually have coverage error of size $n^{-1}$. Most importantly, our work demonstrates a strong link between empirical likelihood and parametric likelihood, since the Bartlett correction had previously only been available for parametric likelihood. A general formula is given for the Bartlett correction, valid in a very wide range of problems, including estimation of mean, variance, covariance, correlation, skewness, kurtosis, mean ratio, mean difference, variance ratio, etc. The efficacy of the correction is demonstrated in a simulation study for the case of the mean.

Article information

Ann. Statist., Volume 19, Number 2 (1991), 1053-1061.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62A10
Secondary: 62G05: Estimation

Bartlett correction chi-squared approximation empirical likelihood ratio statistic nonparametric confidence region signed root empirical likelihood ratio statistic


DiCiccio, Thomas; Hall, Peter; Romano, Joseph. Empirical Likelihood is Bartlett-Correctable. Ann. Statist. 19 (1991), no. 2, 1053--1061. doi:10.1214/aos/1176348137.

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